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The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by
replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc..

What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?

Sliced

Stage: 4 Challenge Level:

Slice the tetrahedron in two with a cut through the line $b$ and
one of the equal edges. The perpendiculars are very important
because of what you need to find the volume of a pyramid. You now
have two identical pyramids like this:

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.